To find the measures of the two vertical angles given as \( (6x - 15)° \) and \( (4x + 5)° \), we can set the two expressions equal to each other since vertical angles are equal.
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Set up the equation: \[ 6x - 15 = 4x + 5 \]
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Solve for \( x \):
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First, subtract \( 4x \) from both sides: \[ 6x - 4x - 15 = 5 \] \[ 2x - 15 = 5 \]
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Next, add 15 to both sides: \[ 2x = 20 \]
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Now, divide by 2: \[ x = 10 \]
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Now, substitute \( x \) back into one of the angle expressions to find the measure of the angles:
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Using the first angle: \[ 6x - 15 = 6(10) - 15 = 60 - 15 = 45° \]
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Using the second angle: \[ 4x + 5 = 4(10) + 5 = 40 + 5 = 45° \]
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Therefore, both angles measure \( 45° \).
The measure of each angle is 45°.